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Simplifying x2 + -100x + 2401 = 0 Reorder the terms: 2401 + -100x + x2 = 0 Solving 2401 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2401' to each side of the equation. 2401 + -100x + -2401 + x2 = 0 + -2401 Reorder the terms: 2401 + -2401 + -100x + x2 = 0 + -2401 Combine like terms: 2401 + -2401 = 0 0 + -100x + x2 = 0 + -2401 -100x + x2 = 0 + -2401 Combine like terms: 0 + -2401 = -2401 -100x + x2 = -2401 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -2401 + 2500 Reorder the terms: 2500 + -100x + x2 = -2401 + 2500 Combine like terms: -2401 + 2500 = 99 2500 + -100x + x2 = 99 Factor a perfect square on the left side: (x + -50)(x + -50) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + -50) equal to 9.949874371 and -9.949874371.Subproblem 1
x + -50 = 9.949874371 Simplifying x + -50 = 9.949874371 Reorder the terms: -50 + x = 9.949874371 Solving -50 + x = 9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 9.949874371 + 50 Combine like terms: -50 + 50 = 0 0 + x = 9.949874371 + 50 x = 9.949874371 + 50 Combine like terms: 9.949874371 + 50 = 59.949874371 x = 59.949874371 Simplifying x = 59.949874371Subproblem 2
x + -50 = -9.949874371 Simplifying x + -50 = -9.949874371 Reorder the terms: -50 + x = -9.949874371 Solving -50 + x = -9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -9.949874371 + 50 Combine like terms: -50 + 50 = 0 0 + x = -9.949874371 + 50 x = -9.949874371 + 50 Combine like terms: -9.949874371 + 50 = 40.050125629 x = 40.050125629 Simplifying x = 40.050125629Solution
The solution to the problem is based on the solutions from the subproblems. x = {59.949874371, 40.050125629}
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